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A299471
Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices.
17
1, 1, 1, 1, 4, 1, 1, 41, 11, 1, 1, 768, 958, 26, 1, 1, 27449, 1042642, 32596, 57, 1, 1, 1887284, 34352419335, 34359509614, 2096731, 120, 1, 1, 252522481, 72057319189324805, 1180591620442534312297, 72057594021152435, 268434467, 247, 1, 1, 66376424160
OFFSET
1,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..91 (rows 1..13)
Wikipedia, Hypergraph
FORMULA
T(n, k) = Sum_{d = 0..n} (-1)^(n-d)*binomial(n,d)*2^binomial(d,k).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 4, 1;
1, 41, 11, 1;
1, 768, 958, 26, 1;
1, 27449, 1042642, 32596, 57, 1;
...
MATHEMATICA
Table[Sum[(-1)^(n-d)*Binomial[n, d]*2^Binomial[d, k], {d, 0, n}], {n, 10}, {k, n}]
PROG
(PARI) T(n, k) = sum(d = 0, n, (-1)^(n-d)*binomial(n, d)*2^binomial(d, k)) \\ Andrew Howroyd, Jan 16 2024
CROSSREFS
Columns 1..4 are A000012, A006129, A302374, A302396.
Row sums are A306021.
The unlabeled version is A301922.
The connected version is A299354.
Sequence in context: A158390 A228836 A176419 * A102602 A156951 A357052
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jun 18 2018
STATUS
approved